On Bartók's Comparative Musicology as a Resource for ......his own music, Bartok was prolific in...

On Bart?k's Comparative Musicology as a Resource for Bart?kian Analysis

Edward Gollin

B?la Bart?k's reticence about his compositional methods is well known. In his essays, 'analytical' comments about his own music rarely delve beyond obvious surface features of the works, generally offering little more than a formal plan or identifying a few

themes. Bart?k eschewed discussion of his compositional techniques, feeling little need to explain the inner workings of his

music?a good composition, he believed, should stand on its own merits.1 But in contrast to the dearth of substantive writing about his own music, Bartok was prolific in his writings about folk music. Numerous essays discuss characteristics of Hungarian and neighboring folk musics; introductions written for his various published folk music collections present the distillation of his 'scientifically' culled data about rhythmic, metric, melodic and

modal features of the collected tunes.

The present article argues that the activities surrounding Bart?k's study and comparison of folk music?in particular his sorting and categorizing collected Hungarian folk tunes?are also analytical activities. These activities, moreover, have ramifications, not only for the corpus of folk tunes for which they were created and applied, but also for Bart?k's original compositions. The paper examines how two aspects of Bart?k's lexical system for classifying and categorizing Hungarian folk tunes?namely caesura tone scheme and syllabic scheme?underlie the variation technique in

ballade" from 15 Hungarian Peasant Songs and play a role in the harmonic and formal design of "Song," No. 116 from

Mikrokosmos?

1 On the attitudes, reliability and limitations of Bartok's comments about his own music, see Somfai 1996,9-24.

2 Bart?k details aspects of his system of tune classification in a number of sources,

including the introduction to Bart?k 1959 and the preface to Bart?k/Kod?ly 1923. The most thorough description of the system is presented in the introduction to Bart?k [1931] 2002, from which the present discussion is drawn. Many studies, particularly by Hungarian scholars, have addressed folk influences in Bartok's

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60 Int?gral

Bart?k's lexical system for tune classification is a modified version of one set forth by the Finnish ethnomusicologist Ilmari Krohn.3 In the modified system, all tunes are transposed to end on G4 to facilitate comparison. Tunes are then classified according to 1) the number of text lines they set (each text line corresponds to one melodic section), 2) the relative height of their melodic section endings (caesurae), 3) the number of syllables in each text line, and 4) their ambitus. Since tunes with four lines/melodic sections by far predominate in the Hungarian folk song repertoire, the present discussion will restrict itself to four-line tune structures and will

only address Bart?k's system of sorting by the height of melodic line-endings and his syllabic classification.

Example 1 illustrates Bart?k's numerical system for denoting line-ending (caesura) tones. G4, the designated finalis of all tunes, is labeled with the Arabic numeral 1. Uninflected steps above G4 are labeled with Arabic numerals, those below G4 are labeled with Roman numerals. Accidentals (# or l>) are used to represent chromatic inflections relative to the 'white note' gamut. Closed and open boxes around the numerals distinguish caesura tones of the different line/melodic sections: the end tone of the first line is

indicated by a downward bracket (i i); the end tone of the second line (the main caesura in a four-line tune) is indicated by a closed box (D); and the end tone of the third line is indicated by an upward bracket (I_I). Since the final tone of the fourth line, by convention, is always on scale step 1 (G4), it requires no explicit notation.4

music; among numerous others, Kovacs 1993 and Suchoff 1984 discuss Bart?k's activities as a collector of folk music; Lampert 1982 and Dobszay 1982 discuss issues surrounding the inclusion of folk-tunes in Bart?k's music; Rice 2000 and Breuer 1975 discuss rhythmic aspects of folk music as manifest in Bart?k's work. Relative to this large body of literature, the present study is limited in its scope: it considers only certain analytical ramifications suggested by Bart?k's lexical system.

3 Bart?k [1931] 2002, vi, refers the reader to Krohn 1902/3.

4 In later publications (e.g. Bart?k/Lord 1951), Bart?k altered the notation, keeping the box to indicate the main caesura, but using instead a right brace ( ] ) to indicate the first-line caesura, and a left brace ( [ ) to indicate the third-line caesura.


On Bart?k's Comparative Musicology 61

Example 1. Bart?k s numerical system for designating line-ending tones.

Symbo?zed: I II III IV V VI VII 1 2 3 4 5 6 7 8 9 10 11

Examples 2a-d present four of Bart?k's published folk-song transcriptions (nos. 34a, 34b, 44 and 261, respectively, from The

Hungarian Folk Song), which illustrate these notational aspects of the

lexical system. For instance, in the melody of Example 2a, the main caesura occurs on IM, indicated by the symbol IE3 placed above it on the staff, the preceding caesura is on C5, indicated by the symbol placed above it on the staff, and the third caesura is on G4, indicated by the symbol ?b placed above it on the staff. Bartok does not denote the final caesura, since by definition it occurs on 1; the figures ^l&L are sufficient to describe the caesura scheme of the tune in Example 2a, a scheme projected also by the tune of Example 2b. Example 2c projects the caesura scheme >3'1 ^.IW; Example 2d projects the caesura scheme ^GDiiL. For the actual sorting, Bartok grouped tunes first according the height of their main caesura, ordered from lowest to highest tone (e.g. tunes with the main caesura E9 precede those with GO). Tunes within each group were then sorted into subgroups based on the height of their first-line caesura, also ordered from lowest to highest. Finally, each subgroup with identical tones at the ends of their second and first lines were subdivided according to the height of their third-line endings, ordered from lowest to highest tone.

Bartok further divided his collected folk tunes by creating groups based upon the number of syllables per line of set text. In the typically syllabic settings of the folk tunes, the number of syllables per line is generally equal to the number of notes per melodic section. Tunes are classified most broadly into isometric tunes (tunes with the same number of syllables per line) and heterometric tunes (tunes that set text lines of different syllabic


62 Int?gral

Example 2. Four tunes from The Hungarian Folk Song (a) 34a; (b) 34b; (c) 44; (d) 261. Translations from Bartok [1931] 2002.

Tempo giusto Vesto (B?k?s), 1918

?3l

An - go - li (Borb?la Angoli

la Kis szok - ny?t va bought a little frock,

m E - l?l kur - t?b (the front bacarne rather short,

bo - dott, Ha - tul hosz - szab - bo - dott. the back became rather long.)

I. Fels?iregh (Tolna), 1906

S?m ?gy-szer, sem k?t - szer, Ha-n?m ti - z?n - k?t - szer. not once, not twice, but twelve times.)

II. Nemes?csa (Kom?rom), 1913

c) Tempo giusto '1,3'

il m Le - fe - k?d - tem csak a - lig, (I lie barely poised on the bed.

,V1I,

Nem e - g? - szen not quite against the wall;

a fa - lig;

J?l meg - ? - lelj en - ge - met, throw your arm well around me.

Le ne es - sem lest I fall down.)

mei - l? - led!

1. ?riszentp?ter (Vas)

Du-na-par-ton van egy ma-lom, Bu-b?-na-tot ?l-nek a-zon, e-je-ha! (By the Danube there's a mill that grinds worries to shreds, hey ha!

N?-kem is van bu - b? - na-torn, O-da-vi-szem, le - j? - ra-torn, e-je-ha! / liave many worries, 17/ take them there and have them ground, hey ha!)


On Bart?k's Comparative Musicologa 63

length).5 Isometric tunes are subdivided according to the specific number of syllables per line. Examples 2a and 2b are six-syllable isometric tunes; each of the four text lines has six syllables and each melodic section contains six notes. Example 2c is a seven syllable isometric tune. Other isometric tunes have eight syllables per line, nine syllables per line, and so on. Heterometric tunes are sub-classified not by the absolute number of syllables per line, but rather by the relative syllabic lengths of their lines. Bart?k observed that heterometric tunes typically had lines of only two different syllable lengths. Symbolizing the longer line with an upper-case and the shorter line by a lower-case z, Bart?k classified heterometric tunes into groups such as , , , (the first and third lines, which have the same length, are longer than the second and fourth lines, which have the same length), , , , (the first two lines, which have the same length, are longer than the last two lines, which have the same length), and so on. Example 2d illustrates a heterometric tune that belongs to the , , , class; it has the specific syllable scheme 8,11, 8,11 over its four sections.

Bart?k used the categories of his lexical system to statistically define characteristics of the Hungarian folk repertoire, to distinguish styles in that repertoire (old- versus new-style melodies) and to compare and identify similarities between Hungarian tunes and those of neighboring regions (e.g. Slovak, Romanian, and Yugoslavian tunes).6 But at its most basic level, Bart?k's lexical system offered the means to catalog his collected melodies so that tunes with similar structural features would be placed in close

5 This use of the terms isometric and heterometric is Bart?k's, and does not connote

traditional meanings of "meter" in the either the qualitative or quantitative (i.e.

long/short) poetic/musical senses. Rather, it simply refers to numbers of syllables/notes per line.

6 Bart?k [1931] 2002 reflects the division of tunes into style classes. Tunes designated as "old style," Bart?k's class A, are presented first, class tunes, the "new style," are presented next, followed by tunes of class C (those that fit into neither category). Bart?k discusses the structural and stylistic distinctions within Hungarian folk music and between Hungarian folk music and folk music of neighboring regions in his 1934 essay "Hungarian Folk Music and the Folk Music of Neighboring Peoples" translated and reprinted in Bart?k 1997,174?240.


64 Int?gral

proximity to one another, to aid the identification of tune variants.

For instance, Bartok recognized the tunes in Examples 2a and 2b?tunes collected twelve years apart in geographically distinct regions of Hungary?to be variants of one another, despite their differing contours and texts, because they have the same syllabic structure and exhibit the same caesura scheme.8

More important for present purposes than Bart?k's specific conventions for ordering the tunes within his lexical system, however, is what the system reveals about Bart?k's structural biases: the system reflects structural categories and structural attributes of the tunes that Bart?k deemed significant for the repertoire. Moreover, certain of those categories?specifically, line-ending scheme and syllabic line length?are not especially familiar to Western analytical practice, which is more inclined to invoke incipits or phrase contour in discussions of tune relatedness.

We shall see presently that awareness of, and attendance to, the structural categories of Bart?k's lexical system in his own compositions?in particular, compositions that feature folk or folk-like melodies?can offer insights into the works.

One fairly well-known way that Bart?k's study and classification of folk material manifests itself in his composition is in his creation of original melodies in imitation of folk tunes. An awareness of the structural categories of Bart?k's classification system can provide the basis for a precise understanding of the relation between the originally-composed and the extant folk

melodies. Example 3a presents the slow, parlando-rubato tune of

7 That the quantitative, scientific/structuralist approach of Bart?k's modified Krohn system bears a similarity in spirit and method to the numerical scheme for classifying folk tales that emerged in the eariy decades of the twentieth century in the work of Finnish folklorist Antti Aarne (known now as the AT-numbering system), is not coincidental: Aarne's teachers, Julius Krohn and Kaarle Krohn,

were father and brother, respectively, of Ilmari Krohn, and were pioneers in the scientific study of folklore. Aarne's system is presented in his 1910 Verzeichnis der

M?rchentypen, revised as Aame 1927.

8 Complete identity of line-ending scheme was not a necessary condition for designating tunes as variants. Bart?k believed the main caesura to be the least malleable of the internal line endings and therefore the most likely caesura to be shared by variant tunes. Tunes 33a and c in Bart?k [1931] 2002, for example, have only the main caesura in common.



Bart?k's "Evening in Transylvania," from his Ten Easy Pieces. The melody does not quote an actual folk tune, but was composed by Bart?k in imitation of one.9

Bart?k's reference to Transylvania in the tide does not simply evoke place, but also style. Prior to World War I, Transylvania was geographically and politically part of Hungary. It was (and still is) home to a Magyar-speaking population (the Sz?kely Hungarians) who were separated from the larger, contiguous Magyar-speaking region to the west, a population that remained culturally and linguistically distinct from the populations of the Romanian-dialect regions that surrounded them geographically. Bart?k postulated that because of the geographic isolation of the Transylvanian

Hungarians, their folk-music repertoire represented the old style of Hungarian folk music in its least corrupted form.10

Attributes of the old-style are evident in the tune Bart?k composed. The pentatonic, parlando-rubato tune from "Evening in Transylvania" is a four-line, 8-syllable isometric melody, a syllabic structure Bart?k considered to be among the oldest.11 Moreover, the tune exhibits a non-architectonic design (i.e. no formal repetition or transposition of melodic sections) and features an overall descending line-ending scheme ^GDlLj (Bart?k's symbology has been transposed on Example 3a to reflect the final on E); both are features of the old style.

9 Bartok himself says of the work that it is "an original composition.. .with themes

of my own invention...in the style of...the Hungarian-Transylvanian folk tunes. There are two themes. The first one is a parlando rubato.. .an imitation of song, a vocal melody." The comments were made during an interview with David Le Vita as part of the "Ask the Composer" series, in conjunction with a concert at the Brooklyn Museum on July 2, 1944, broadcast by radio station WNYC. The interview has been released on the CD "Bartok Recordings from Private Collections" (Hungaroton 12334/7, 1995). A transcription of the interview is published in Kro? 1969. Parlando rubato, a performance style in which a tune is sung in an unmeasured rubato, is one of the two performance types Bart?k identified in Hungarian folk music. The other, tempo guisto, refers to tunes performed in rhythm at a fixed tempo.

10 Bart?k [1931] 2002, xix.

11 Bart?k [1931] 2002, xxxv.


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Example 3. (a) The slow melody from 'Evening in Transylvania.

(b) Tune no. 3 from "Sz?kely ballad?k. "

(c) Tune no. 5c from "Sz?kely ballad?k. "


On Bart?k's Comparative Musicol?gy 67

While it may be that the titular reference to Transylvania intends nothing deeper than the evocation of the old style, it is curious that Bart?k places the main caesura of his tune on S, a notably uncommon main-caesura tone. Bart?k observed in The Hungarian Folk Song that tunes with the main caesura on were found in only seven of 70 eight-syllable isometric tunes.12 However, most of these tunes are found within the geographic region that includes Transylvania?exclusively so in about half the cases. In other words, main caesuras on ED, while infrequent in the total corpus of Hungarian folk tunes, are nonetheless most typically found in tunes from the Transylvanian region.

Although Bart?k includes no examples of tunes in The Hungarian Folk Song that have the exact scheme ^EOdL, an example exists in Bart?k's earliest published folk song collection, "Sz?kely ballad?k" (Sz?kely Ballads): Example 3b presents the six syllable isometric tune "Magyar?sy Tam?s," number 3 in the collection.13 Example 3c presents number 5c from "Sz?kely ballad?k," an eight-syllable isometric tune that exhibits the related scheme ^GDlIj, and which shares certain contour features of the tune from "Evening in Transylvania."14 Line-ending scheme is, to be sure, only one attribute of a given tune, and a myriad of other collected tunes could be called forth that bear similarity in other ways to the slow melody of "Evening in Transylvania." Rather than claiming that Bart?k crafted the melody of "Evening in

Transylvania" as an explicit or intentional variant of these or any other particular tunes, I simply suggest that recognizing how the melody exhibits specific structural attributes of tunes found primarily in the Transylvanian region?a descending line-ending scheme with main caesura on H?is one way of explaining how

12 Bartok [1931] 2002, xix. Melodies with the same main caesura are found in similarly low proportion among tunes of the other isometric syllabic classes: three out of 30 six-syllable tunes, four out of 35 eleven-syllable tunes, and so on.

13 Bartok 1908. The article is reprinted in Bartok 1966, 15-50. Bartok included "Magyar?sy Tam?s," in his later collection, Transyhanian Hungarians: Folk Songs

(Bart?k/Kod?ly 1923), reprinted in Bart?k 1997, 77-134, along with three other tunes exhibiting the scheme ^G?lL, all from Cs?k County, Transylvania (see

melodies 121-124).

14 Concerning the relatedness of nines with common main caesura, see note 8.


68 Int?gral

Bart?k's original tune projects a distinctively Transylvanian character.

Whereas the original melody of "Evening in Transylvania" may be understood as a variant, in a general or idealized sense, of a class of actual folk tunes, Bart?k explores variation in a more concrete sense in "Ballade," from 15 Hungarian Peasant Songs. The work takes as its theme the tune "Angoli Borb?la," presented in Example 2a. The piece begins with an unaccompanied statement of the tune-as-theme in octaves; subsequent statements (variations 1-4, 8-9) preserve the tune as a melody, adorning it with a variety of melodic, arpeggiated or chordal accompaniments. Although the movement is one of Bart?k's few works explicidy designated as a theme and variations (Bart?k writes in parentheses beneath the tide, "tema con variazioni"), the technique of presenting several statements of a folk tune with varied accompaniments occurs repeatedly throughout Bart?k's output?in For Children, Rumanian Christmas Carols, and the Improvisations Op. 20, to name only a few.15

However, Bart?k explores a different variation technique in the middle variations of ballade," one that presents variations of the tune itself.

Example 4 presents the theme of "Ballade" aligned above variations 5?7. The example illustrates how Bart?k stricdy preserves the ^IESlL line-ending scheme in each variation, despite changes in key, register, meter and rhythm. The example underscores the importance Bartok placed upon the line-ending scheme?rather than on melodic contour?as a determinant of tune relatedness. For instance, the second melodic section of the

tune begins with an ascent to scale degree seven, but there is no ascent in the corresponding sections of variations five or six; the second section of variation five does not even include the fifth

scale degree, the initial tone of that section in the original tune. The last melodic section of the fifth variation similarly lacks the melodic ascent found in the corresponding section of the original tune.

15 No. 29, for example, from the Hungarian collection of For Children similarly states its tune in octaves before presenting the tune three more times with varied accompaniments.



-a I

! ?3

5 - -, , : S S? Hl1 |

1 ? ? ^ I ' ; .. s ,L-- u... 13 '~' ^ \? -

s H ?, ....

? : : : 01 ? ::: ?;

t*33 ::: "

^ m?r ^ inrr *cf?p > Fri


70 Int?gral

Instead of maintaining an overall descent to the final in the last section of the sixth variation, Bartok substitutes a formula pentatonic cadence, 4-43-47?1, that approaches the final from below.16 Such differences in contour are not unlike the differences

Bartok encountered among tune variants in the collected folk repertoire itself. For instance, the variant of "Angoli Borb?la" given as Example 2b, "K?rettelek t?ged," lacks the former's initial ascending fifth; the second melodic section of "K?rettelek t?ged," moreover, has the purely descending contour observed in variations five and six of "Ballade."

Notable in ballade" is the syllabic progression of variations 5 7, presenting four- then five- then seven-syllable isometric versions of the original six-syllable isometric tune. The progression suggests a realization, in compositional practice, of a process of rhythmic division through which, Bart?k hypothesized, folk tunes evolved over time. In The Hungarian Volk Song after having discussed eight syllable, six-syllable and seven-syllable isometric old-style tunes, Bart?k presents a summary diagram of three rhythmic schemes, reproduced as Example 5. Bart?k suggests that the second scheme possibly derives from the first through a merging of the last two eighths into a single quarter note; the third scheme, he suggests, possibly derives from the second by a similar merging of the last pair of eighths into a single quarter note. Bart?k concedes, however, that the process could have proceeded in the opposite direction, that seven-syllable tunes could have evolved (via a rhythmic splitting of tones) from six-syllable tunes, and eight syllable tunes from seven-syllable tunes.17 It is curious that the Ballade variations reenact this hypothetical evolutionary process, in which Bart?k resituates the original tune as an intermediate stage in a progression from a four-syllable skeleton to a fleshed-out, seven syllable version.18

16 On pentatonic formulae in Hungarian folk music, see Kod?ly 1970.

17 Bart?k [1931] 2002, xxix.

18 Because 4- and 5-syllable nines do not exist in the old style Hungarian repertoire, variations 5 and 6 are truly products of art in the same way that the 4 syllable isometric pentatonic quatrain that opens Bluebeards Castle is an 'artificial' creation. Another work that explores metric/syllabic tune variations is "Stamping Dance," no. 128 from Mikrokosmos vol. 5. The work presents an originally



Example 5. Rhythmic schemes underlying Bart?k s proposed stages of rhythmic evolution in isometric folk tunes.

IJ7T31JTJ1II

? JTT31J J II

While Bart?k's compositional sensitivity to structural attributes such as line-ending and syllabic scheme was evident when he created tunes in imitation of Hungarian folk style, analytical attendance to the structural categories of his lexical system can offer insights into Bart?k's 'progressive' compositions as well. We conclude with an examination of "Song," No. 116 from

Mikrokosmos vol. 4.

Table 1 presents an outline of the work's formal divisions. The piece is strophic, comprising three statements of a four-section melody: the initial statement (statement A, mm. 8-15) presents the unaccompanied melody in octaves; statement (mm. 16-24) presents the melody in the left hand against a countermelody in the ' right; statement C (mm. 28-35) presents the original melody in the right hand with a chordal accompaniment in the left.19 The

melodic statements are framed by three march-like passages. The march music opens the work (mm. 1-8), concludes the work (mm. 36-43), and constitutes a brief interlude between statements and C (mm. 24-28). The work is G-centric: the opening bass gesture

composed, 7-syilable isometric tune, with the fixed caesura scheme '^'IW^ (mm. 5-12). Later statements of the tune include a 6-syllable variant (mm. 13-20), a 4 syllable variant (L.H., mm. 28-35), and finally a freer "11-syllable" variant, with extended ending (mm. 47-66).

19 The and C statements of the melody feature minor changes relative to the opening statement. In the third section of statement B, the third and eleventh tones are chromatically inflected (El? instead of and Cl instead of C\ respectively). Bart?k alters the last section of the melody in the final statement, replacing the initial rising line, F-G-A, with a turn, A-G-A, presumably to avoid a collision between the melody and the chromatically descending chords of the accompaniment.


72 Int?gral

a o

O S O

O

a e* o

U

O

o u o

8 O

cg

O

.s

a o

O

M a CU

1 ce M C/3

U

G

r o ?s

fl

O

1 a

e ci 4?> c/3

00 IT)

00

TT (

00 (

LO CO 00 CN


On Bart?k's Comparative Musicol?gy 73

_Jft? jt^ ail IL1 ~V \j% il"

V ^ ti ? ^ ?t Fi -i iff. ?:l ? fit* V ? " ^ " ?- :

^ { ~\ 'S "* I_I

I E :

I t ?

- - -xt -i ? "

-r1? ^ till -a

74 Int?gral

arrives on a G final at mm. 2 and 4 from the encircling 4 and 17 (F and C), a formulaic cadential gesture in the G-Hungarian pentatonic.20 C asserts itself as a contrasting center (as subdominant?) in the march introduction at mm. 5?8, and again at the march interlude of mm. 24?28. In both cases, melodic closure

of the march passages on C coincides with the opening C of the melody in the A and C statements, preparing the entries and eliding the sectional divisions. G returns as tonal center in the final march

music (mm. 36-43) and the work closes on a G-major triad. The centricity of G is fortified by the main melody's closure on G; closure of the countermelody on C fortifies the work's principal C? G conflict.

Example 6 presents the work's melody and countermelody. Despite their contrasting finals, the melody and countermelody share a number of similarities. Both melody and countermelody have a four-section structure, and parallel sections feature similar contours and gestures. Melody and countermelody are both heterometric, and although they project different syllabic schemes?the melody belongs to the 2, 2, Z, 2 class (11, 11, 13, 11 syllables), the countermelody to the 2, 2, , class (9, 9, 14, 14 syllables)?they may be viewed as variant partitions of the same 46 'syllable' total.21 Moreover, as Example 6 illustrates, the line-ending schemes of the melody and countermelody, while not identical, share similar?but mis-ordered?scale-step content: the melody comprises endings on t7,1>3 and 2, the countermelody on l>7, V? and

Yet whereas the line-ending schemes are distinct in chromatic pitch space, the unordered tone schemes are identical when viewed in octatonic step space. Example 7 illustrates a new labeling system

20 Kod?ly 1970.

21 Although it is curious that of the melody and countermelody comprise the same

number of 'syllables/ Bart?k never discusses total syllabic length as a topic in his folk-melody categorical schemes.

22 Technically, the Bl> caesura of the countermelody corresponds to the "uninflected" 7 in the transposed labeling system, since the labels correspond to tones in a mixolydian octave species. I have used the \> and t symbols to underscore the use of two different forms (raised and lowered) of degree 7 in the two melodies.



Example 7. labeling system from G) for line-ending tones in the C?G octatonic collection.

Symbolized in octatonic step space: 1 2 3 4 5

? y ?=d= 10 11 12

analogous to that of Example 1 using as steps tones of the C?G octatonic collection.23 Although Bartok, in his writings on folk music, never proposes an eight-step octatonic scale system upon which to map melodies, it is curious that he did consider non diatonic scale systems for the representation of certain repertoires. In the introduction to Serbo-Croatian Folk Songs, Bartok identifies a number of narrow-range chromatic melodies in which each chromatic tone represents, not an inflection or colored form of a diatonic scale degree, but rather an "independent degree" in a chromatic scale.24

Example 8 maps the caesura schemes of the melody and countermelody (reckoned from finals on G and C respectively) onto the C-G octatonic labeling system of Example 7, revealing the equivalence of the unordered collections in octatonic step space. While the schemes are not octatonic complements, the melody and countermelody schemes together cover seven of the eight tones of the C?G octatonic collection: G, A, Bl>, C, Dt, Et and Fl

23 The C-G octatonic refers to the octatonic collection that uniquely embeds both G and C

24 Bart?k/Lord 1951, 61?64. Gillies 1983 discusses certain analytical ramifications of these melodies.

25 The unordered schemes are equivalent under the "T3" transformation in octatonic step space?the transformation that maps tones of an octatonic collection to the those tones three steps higher in the scalar ordering of that octatonic collection, regardless of the specific chromatic distances involved. In the C?G octatonic collection of "Song," octatonic-T3 takes G to C, A to Dl>, Bl? to El?, and so on, mapping tones of the melody's line-ending scheme onto those of the countermelody's scheme.


76 Int?gral

Example

On Bart?k's Comparative Musico?ogy 77

While neither the melody nor countermelody of "Song" could be considered 'octatonic' melodies, it is curious to observe certain

of their features in light of the C-G octatonic collection projected by their line-ending schemes. For example, the descending thirds leading to the first and second caesurae of the melody (C-A-Ftt and E-Ct-A) exclusively unfold five tones of the C-G octatonic; the fourth line of the countermelody unfolds exclusively over five tones of the C-G octatonic (A, Bt, C, Dt, and Et).

More striking, however, is the reflection of the linear structures

unfolded by the line-ending schemes in the work's vertical, or harmonic, structure. For example, Bart?k vertically projects tones of the C-G octatonic collection in the accompaniment to the third statement of the melody at mm. 29-31, setting the first two sections of the melody against an accompaniment comprising C

minor, C-major and Ct-diminished triads. The triads exhibit no clear tonal function, but rather are exclusively constituted by tones of the C-G octatonic collection. A more direct relationship between the linear and vertical structure is illustrated in Example 9, a transformational network involving the line-ending scheme of the countermelody and certain chords prominent in the march music. A vertical arrow labeled "To" on Example 9 reveals that the tones of the countermelody caesura scheme exhibit pitch-class identity with tones of the [013] and [025] trichords, {C, Bt, Dt} and {C, Bt, Et}, that constitute the ?subdominant' march music. That is, the countermelody scheme is vertically manifest in the subdominant march chords, and, via transposition by , manifest in the 'tonic' versions of those trichords, {G, F, At} and {G, F, Bt}, salient at the opening and closing march interludes.

While other studies have discussed the stylistic and aesthetic influence of Bart?k's ethnomusicological activities on his original compositions, the present paper argues that those activities can offer specific analytical insights as well. Bart?k's work as a comparative musicologist entailed modes of analysis and attention to structural domains largely foreign to Western music theories, and awareness of those modes and the structural domains they reveal can offer insights to his music. We have seen, for example, how Bart?k uses the line-ending scheme of the tune in "Ballade" as an invariant structure in variations 5-7 while varying the syllabic


78 Int?gral

structure of the isometric source tune. In "Song," the 'syllabic' structure both unifies and differentiates the untexted melody and

countermelody: both comprise a total of 46 syllables, yet each partitions those totals according to different heterometric schemes. Line-ending scheme in "Song," moreover, offers a significant means of segmenting tones in the pitch domain. In particular, reflection of the (linear) countermelody caesura scheme in the (vertical) trichords of the march music unifies melodic and harmonic aspects of the work.

References

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On Bart?k's Comparative Musico?ogy 79

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Issue Table of ContentsIntégral, Vol. 22 (2008) pp. 1-180Front MatterSchenker's Organicism Revisited [pp. 1-58]On Bartók's Comparative Musicology as a Resource for Bartókian Analysis [pp. 59-79]Tonal Functions and Active Synthesis: Hugo Riemann, German Psychology, and Kantian Epistemology [pp. 81-116]Fluidities of Phrase and Form in the "Intermezzo" of Brahms's First Symphony [pp. 117-143]ReviewEntendez-vous la musique? [pp. 145-173]

Letters to the Editors [pp. 175-177]Back Matter

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